Question

make a table of values for the following equation. then graph the equation.
$y = |x + 5|$
(simplify your answers.)
graph the equation $y = |x + 5|$. choose the correct graph below.
a. graph b. graph c. graph d. graph
help me solve this view an example get more help -
clear all final check
review progress question 8 of 26 back next

Explanation:

Part 1: Table of Values for \( y = |x + 5| \)

To create a table of values, we choose several values for \( x \) and calculate the corresponding \( y \)-values using the absolute value function.

Step 1: Choose \( x \)-values

Let's pick \( x = -7, -6, -5, -4, -3 \) (values around the vertex of the absolute value graph, which occurs where the expression inside the absolute value is zero, i.e., \( x + 5 = 0 \) or \( x = -5 \)).

Step 2: Calculate \( y \)-values for each \( x \)

• For \( x = -7 \):

\( y = |-7 + 5| = |-2| = 2 \)

• For \( x = -6 \):

\( y = |-6 + 5| = |-1| = 1 \)

• For \( x = -5 \):

\( y = |-5 + 5| = |0| = 0 \)

• For \( x = -4 \):

\( y = |-4 + 5| = |1| = 1 \)

• For \( x = -3 \):

\( y = |-3 + 5| = |2| = 2 \)

Part 2: Graphing \( y = |x + 5| \)

The absolute value function \( y = |x + 5| \) is a V - shaped graph (since the coefficient of \( |x| \) is positive) with its vertex at \( (h, k) \) where the function is in the form \( y = |x - h|+k \). For \( y = |x + 5| \), we can rewrite it as \( y = |x - (-5)|+0 \), so the vertex is at \( (-5, 0) \).

• The graph opens upward (because the coefficient of the absolute value term is positive, \( a = 1>0 \)).
• To the left of \( x=-5 \) (where \( x + 5<0 \)), the function behaves like \( y=-(x + 5)=-x - 5 \) (a line with slope \( - 1 \)).
• To the right of \( x=-5 \) (where \( x + 5\geq0 \)), the function behaves like \( y=x + 5 \) (a line with slope \( 1 \)).

Looking at the options:

• Option A: The vertex is at \( (-5, 0) \), the left side has a negative slope, and the right side has a positive slope, which matches the behavior of \( y = |x + 5| \).

Table of Values:

\( x \)	\( y =	x + 5	\)
-6	1
-5	0
-4	1
-3	2

Final Answer for Graph:

A. (The graph with vertex at \( (-5, 0) \), opening upward, with left - hand slope \( - 1 \) and right - hand slope \( 1 \))

Answer:

Part 1: Table of Values for \( y = |x + 5| \)

To create a table of values, we choose several values for \( x \) and calculate the corresponding \( y \)-values using the absolute value function.

Step 1: Choose \( x \)-values

Let's pick \( x = -7, -6, -5, -4, -3 \) (values around the vertex of the absolute value graph, which occurs where the expression inside the absolute value is zero, i.e., \( x + 5 = 0 \) or \( x = -5 \)).

Step 2: Calculate \( y \)-values for each \( x \)

• For \( x = -7 \):

\( y = |-7 + 5| = |-2| = 2 \)

• For \( x = -6 \):

\( y = |-6 + 5| = |-1| = 1 \)

• For \( x = -5 \):

\( y = |-5 + 5| = |0| = 0 \)

• For \( x = -4 \):

\( y = |-4 + 5| = |1| = 1 \)

• For \( x = -3 \):

\( y = |-3 + 5| = |2| = 2 \)

Part 2: Graphing \( y = |x + 5| \)

The absolute value function \( y = |x + 5| \) is a V - shaped graph (since the coefficient of \( |x| \) is positive) with its vertex at \( (h, k) \) where the function is in the form \( y = |x - h|+k \). For \( y = |x + 5| \), we can rewrite it as \( y = |x - (-5)|+0 \), so the vertex is at \( (-5, 0) \).

• The graph opens upward (because the coefficient of the absolute value term is positive, \( a = 1>0 \)).
• To the left of \( x=-5 \) (where \( x + 5<0 \)), the function behaves like \( y=-(x + 5)=-x - 5 \) (a line with slope \( - 1 \)).
• To the right of \( x=-5 \) (where \( x + 5\geq0 \)), the function behaves like \( y=x + 5 \) (a line with slope \( 1 \)).

Looking at the options:

• Option A: The vertex is at \( (-5, 0) \), the left side has a negative slope, and the right side has a positive slope, which matches the behavior of \( y = |x + 5| \).

Table of Values:

\( x \)	\( y =	x + 5	\)
-6	1
-5	0
-4	1
-3	2

Final Answer for Graph:

A. (The graph with vertex at \( (-5, 0) \), opening upward, with left - hand slope \( - 1 \) and right - hand slope \( 1 \))